This&nbsp; book&nbsp; grew&nbsp; out&nbsp; of&nbsp; courses which I taught&nbsp; at&nbsp; Cornell University&nbsp; andthe University&nbsp; of&nbsp; Warwick during&nbsp; 1969&nbsp; and&nbsp; 1970.&nbsp; I wrote it because&nbsp; of&nbsp; astrong belief&nbsp; that&nbsp; there should be readily available a semi-historical and geo-metrically motivated exposition&nbsp; of&nbsp; J.&nbsp; H. C. Whitehead's beautiful theory&nbsp; ofsimple-homotopy types; that the best way to understand this theory&nbsp; is&nbsp; toknow how&nbsp; and&nbsp; why it was built. This belief&nbsp; is&nbsp; buttressed by the fact that themajor uses of,&nbsp; and&nbsp; advances in, the theory in recent&nbsp; times-for&nbsp; example, thes-cobordism theorem (discussed in&nbsp; §25),&nbsp; the use&nbsp; of&nbsp; the theory in surgery, itsextension&nbsp; to&nbsp; non-compact complexes (discussed&nbsp; at&nbsp; the end&nbsp; of&nbsp; §6)&nbsp; and theproof&nbsp; of&nbsp; topological invariance (given in the&nbsp; Appendix)-have&nbsp; come fromjust such&nbsp; an&nbsp; understanding.A second reason for writing the&nbsp; book&nbsp; is&nbsp; pedagogical. This&nbsp; is&nbsp; an excellentsubject for a topology student&nbsp; to&nbsp; "grow&nbsp; up"&nbsp; on. The interplay betweengeometry&nbsp; and&nbsp; algebra in topology, each enriching the other,&nbsp; is&nbsp; beautifullyillustrated in simple-homotopy theory. The subject&nbsp; is&nbsp; accessible (as in thecourses mentioned&nbsp; at&nbsp; the outset)&nbsp; to&nbsp; students who have&nbsp; had&nbsp; a good one-semester course in algebraic topology. I have tried to write proofs which meetthe needs&nbsp; of&nbsp; such students. (When a&nbsp; proof&nbsp; was omitted&nbsp; and&nbsp; left as an exercise,it was done with the welfare&nbsp; of&nbsp; the student in mind.&nbsp; He&nbsp; should do suchexercises zealously.)There is some new material&nbsp; here1-for&nbsp; example, the completely geometricdefinition&nbsp; of&nbsp; the Whitehead group&nbsp; of&nbsp; a complex in&nbsp; §6,&nbsp; the observations&nbsp; on&nbsp; thecounting&nbsp; of&nbsp; simple-homotopy types in&nbsp; §24,&nbsp; and&nbsp; the direct&nbsp; proof&nbsp; of&nbsp; theequivalence&nbsp; of&nbsp; Milnor's definition&nbsp; of&nbsp; torsion with the classical definition,given in&nbsp; §16.&nbsp; But my debt to previous works on the subject&nbsp; is&nbsp; very great.I refer to [Kervaire-Maumary-deRham], [Milnor&nbsp; 1]&nbsp; and&nbsp; above all&nbsp; [J.&nbsp; H. C.Whitehead&nbsp; 1,2,3,4].&nbsp; The&nbsp; reader should&nbsp; turn&nbsp; to&nbsp; these sources for more material,alternate viewpoints, etc.I&nbsp; am&nbsp; indebted&nbsp; to&nbsp; Doug&nbsp; Anderson&nbsp; and&nbsp; Paul Olum for many enlighteningdiscussions,&nbsp; and&nbsp; to&nbsp; Roger Livesay&nbsp; and&nbsp; Stagg Newman for their eagle-eyedreading&nbsp; of&nbsp; the original manuscript. Also I would like to express my apprecia-tion&nbsp; to&nbsp; Arletta Havlik, Esther Monroe, Catherine Stevens&nbsp; and&nbsp; DoloresPendell for their competence&nbsp; and&nbsp; patience in typing the manuscript.My research in simple-homotopy theory was partly supported by grantsfrom the&nbsp; National&nbsp; Science Foundation&nbsp; and&nbsp; the Science Research Council&nbsp; ofGreat Britain. I&nbsp; and&nbsp; my wife&nbsp; and&nbsp; my children are grateful&nbsp; to&nbsp; them.

A Course in Simple Homotopy Theory PDF

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